Roman Thiele, KTH

Improved wall functions in OpenFOAM

3rd Gothenburg Regional OpenFOAM User Group Meeting

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Overview

• Introduction

• 2 Wall function sets- UMISTA- Laurien's thermal wall function

• Implementation of the two wall functions

• Status/Summary/Questions

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Heat transfer in SCW

• Strong variations around pseudo critical point

• Computationally challenging- LRN computations- Thermal wall

functions

Source: Maria Jaromin, Lic. Thesis, 2012

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Heat transfer deterioration in SCW

• Work done by Maria Jaromin in CFX

• Deterioration observed under strong heat flux

• Strong variations of thermo- physical properties and buoyancy effects close to the wall

Source: Maria Jaromin, Lic. Thesis, 2012

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UMISTA wall function

•How does it work- Analytical integration of the boundary layer equations through viscous and logarithmic layer

•Several versions available- Simplified version, give same results as full temperature variation and is simpler

- T varies linearly from wall to viscous sublayer edge and from viscous sublayer edge to opposite edge of cell

- Parabolic description of the molecular viscosity in the viscous sublayer

•Inclusion of buoyancy terms and rapidly changing properties

Source: Aleksey Gersimov, PhD Thesis, 2003

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UMISTA wall function – Mixed Convection Results

Source: Aleksey Gersimov, PhD Thesis, 2003

Buoyancy opposedBuoyancy aided

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Laurien's thermal wall function

• No separate wall function for the velocity as it is assumed that temperature and velocity are decoupled

• Uses temperature varying thermo-physical properties

• Add's variation by probability density function to all variables

• Numerical integration through viscous and logarithmic layer

• Similar to Jayatilleke's wall function (based on turbulent logarithmic layer)

Source: Laurien, Development of Numerical Wall-Functions to Model the Heat Transfer of Supercritical Fluids, 2010

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OpenFOAM framework for SCW

• Super critical water properties missing

• Need to be implemented- Use libraries that exist and are based on different framework →Freesteam and openfoam-ext project

• Employing solver buoyantPimple/SimpleFoam- Buoyancy effect included in momentum equation- Modified to write out property fields of use- Modified to take SCW properties into account

• Work ongoing

Source: www.extend-project.de, http://freesteam.sourceforge.net/

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Implementation of UMISTA

• Original development for 2D staggered mesh with Cartesian coordinates

• OF is 3D, co-located mesh with curvilinear grid and possibility of polyhedral cell

• Restrictions for mesh after implementation- Cells must be hexahedral or prismatic at the boundary layer

• 3 boundary conditions necessary- (wall shear stress implementation)- (turbulent production and dissipation conditions) - (heat flux boundary condition)

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Pseudo algorithm UMISTA – alphat based on q''

1. Calculate to the edge of the cell, yn

2. Read Twall, if not present, use input by user

3. Get initial Tv, by taking mean between and TP and Twall

4. Calculate all value dependent on Twall and Tv

5. Calculate Tvn

6. Calculate Twalln

7. Compare Twalln with Twall

n-1

8. Calculate alphat

Iter

atio

n

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Pseudo algorithm UMISTA – μ

t wall function

• OF introduces wall shear stress through turbulent viscosity at the wall into the momentum equation

1. Calculate Twall and Tv as in temperature wall function

2. Calculate temperature dependent thermophysical values

3. Calculate Un by interpolating the velocity field to the cell surfaces and project the velocity from the opposite face into a parallel plane to the patch face

4. Calculate

5. Calculate

Iteration

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Implementation of Laurien's– alphat based on q''

1.Estimate Tcs through average between wall and first point temperature

2.Retrieve wall temperature from previous time step (pseudo time step) or iteration or from the default value that is given to the wall when using the wall heat flux boundary conditions

3.Calculate Tcs using equation (13)

4.Calculate temperature variation by equation (12)

5.Calculate the dimensionless temperature in point y+P using equation (1)

6.Calculate the variable friction velocity from equation (4)

7.Calculate the wall temperature from equation (7)

8.Compare the wall temperature to the previous wall temperature from previous iteration, if relative difference is smaller than 10-6 then continue

9.Calculate the effective thermal diffusivity

Iter

atio

n

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Status

• Status- Completed implementation and mostly debugging- Water properties• Testing of different implementation strategies ongoing

• TODO:- Testing against DNS/experimental data

• Problems- SCW water properties in OpenFOAM- Hard coded water properties (no low level access to thermal pysical

properties)

Improved wall functions in OpenFOAM

Questions? Suggestions? Problem solved?